Phase 3: Agricultural Commodity Loss Variations across the Pacific Northwest Palouse Region, 1989-2015 - Mixed Modeling Analysis
Erich Seamon
9/25/2018
Introduction
This analysis explores the relationships of agricultural commodity loss, at a county level, from 1989-2015, for the 26 county region of the Palouse, in Washington, Idaho, and Oregon. Here we explore the entire range of commodities and damage causes, identifying the top revenue loss commodities and their most pertinent damage causes - as indicated from the USDA’s agricultural commodity loss insurance archive.
In Phase 3, we perform mixed modeling analysis using a two-step hurdle technique, for apples, wheat, cherries, and dry peas, specifically for a selected set of damage causes. The following analysis builds on Phases 1 and 2, steps 1-8.
Step 9. Individual Commodity Mixed Model Analysis. In Step 9, we perform a mixed modeling analysis, using a two step hurdle model technique to address zero-inflated data.
Step 9: Hurdle Mixed Models
Hurdle model techniques allow us to address zero inflated datasets, by first running a logstical regression model to determine the probability of zeros occuring. Then we use the non-zero values in a separate, mixed model. In this instance, we use county as a random effect.
In our two part hurdle model, we identify zero values - that is, counties and years that have zero loss for particular damage causes for apples. Previously we removed counties that we have determined have no apples being grown - based on known crop yield data. The counties we are identifying are those where we KNOW apples are being grown, but in some instances, there are no loss claims being filed in particular years.
As such, these are not missing data, but actual zero values that we do not want to exclude from our model. However we want to be able to use a normalized distribution that is not positively skewed/zero inflated.
Hurdle Model - APPLES
Here we run our hurdle technique for APPLES, using a generalized linear model with a binomal function to delineate between zero and non-zero values. Given this model, Is our data normally distributed? What (if any) outliers exist? Are residuals well distributed - indicating normality?
## llh llhNull G2 McFadden r2ML
## -294.4881431 -423.9973502 259.0184142 0.3054482 0.3371061
## r2CU
## 0.4557171##
## Hosmer and Lemeshow goodness of fit (GOF) test
##
## data: alllevs2_apples$non_zero, fitted(m1)
## X-squared = 8.3228, df = 8, p-value = 0.4026Now plot this Apples zero/non-zero bionomal model to see outliers and the zeros vs non-zeros.
FIGURE 13: Apples zero/non-zero bionomal model to see outliers and zeros values vs non-zero values.
## GVIF Df GVIF^(1/(2*Df))
## year 1.16 14 1.005
## damagecause 36115.35 5 2.856
## county 14626.71 6 2.224
## damagecause:county 101372467.97 30 1.360## pvalue
## (Intercept) 0.0295511713
## year2012 0.0023203939
## year2014 0.0269850901
## year2015 0.0168428603
## damagecauseFreeze 0.0193224383
## damagecauseFrost 0.0004283115
## countyBenton 0.0081231386
## countyFranklin 0.0193224383
## countyGrant 0.0432144665
## countyUmatilla 0.0193224383
## damagecauseFrost:countyUmatilla 0.0211319984
## damagecauseFrost:countyWalla Walla 0.0027298561Now subset to just those APPLES observations with a loss greater than zero (so all non-zeros), and run a linear regression (switched to log loss due to outliers), to make sure that our residuals and other parameters suggest normality.
## Linear mixed model fit by REML ['lmerMod']
## Formula: log(loss) ~ year + damagecause + (1 | county)
## Data: subset(alllevs2_apples, non_zero == 1)
##
## REML criterion at convergence: 880.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6105 -0.5834 0.1296 0.6039 3.2595
##
## Random effects:
## Groups Name Variance Std.Dev.
## county (Intercept) 0.4085 0.6391
## Residual 1.9353 1.3912
## Number of obs: 252, groups: county, 7
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 10.0015 0.4420 22.627
## year2002 -0.5154 0.4851 -1.062
## year2003 0.7557 0.4627 1.633
## year2004 -0.8494 0.5155 -1.648
## year2005 0.4481 0.4732 0.947
## year2006 0.6558 0.4989 1.315
## year2007 1.3272 0.4906 2.705
## year2008 0.3012 0.5431 0.555
## year2009 1.4475 0.4465 3.242
## year2010 0.6472 0.4902 1.320
## year2011 0.5794 0.4467 1.297
## year2012 0.8257 0.6462 1.278
## year2013 1.9262 0.4366 4.412
## year2014 1.1395 0.5637 2.021
## year2015 1.5109 0.4388 3.444
## damagecauseCold Winter -0.9218 0.5054 -1.824
## damagecauseFreeze 0.1111 0.2829 0.393
## damagecauseFrost 0.1800 0.2760 0.652
## damagecauseHail 0.5523 0.3164 1.746
## damagecauseHeat -0.8392 0.4382 -1.915
Finally, we examine the APPLES model coefficent estimates of our model output.
Finally, we exponentiate the coefficient estimates and confidence intervals for odds ratios.
## rn lower upper estimate stderror
## 1: year2002 0.2391268 1.4963560 0.5972832 1.624263
## 2: year2003 0.8880306 5.1045958 2.1290275 1.588319
## 3: year2004 0.1615692 1.1341296 0.4276712 1.674515
## 4: year2005 0.6405065 3.8317532 1.5653805 1.605139
## 5: year2006 0.7487014 4.9362244 1.9267112 1.646852
## 6: year2007 1.4935220 9.5416645 3.7703541 1.633242
## 7: year2008 0.4834832 3.7669837 1.3514624 1.721279
## 8: year2009 1.8286407 9.8876821 4.2523722 1.562876
## 9: year2010 0.7540950 4.8140575 1.9102689 1.632628
## 10: year2011 0.7656987 4.1456813 1.7849411 1.563145
## 11: year2012 0.6685715 7.7130937 2.2833762 1.908200
## 12: year2013 3.0061651 15.6593281 6.8635179 1.547469
## 13: year2014 1.0759561 9.0617292 3.1250736 1.757155
## 14: year2015 1.9764019 10.3783962 4.5309969 1.550798
## 15: damagecauseCold Winter 0.1529470 1.0333582 0.3977923 1.657642
## 16: damagecauseFreeze 0.6544157 1.9068833 1.1175112 1.327027
## 17: damagecauseFrost 0.7104873 2.0162650 1.1972069 1.317828
## 18: damagecauseHail 0.9559618 3.1613193 1.7373253 1.372203
## 19: damagecauseHeat 0.1888239 0.9893675 0.4320540 1.549873
Hurdle Model - WHEAT
Here we run our hurdle technique for WHEAT, using a generalized linear model with a binomal function to delineate between zero and non-zero values. Given this model, Is our data normally distributed? What (if any) outliers exist? Are residuals well distributed - indicating normality?
## llh llhNull G2 McFadden r2ML
## -1392.6347080 -1967.6122795 1149.9551430 0.2922210 0.3184041
## r2CU
## 0.4357824##
## Hosmer and Lemeshow goodness of fit (GOF) test
##
## data: alllevs2_wheat$non_zero, fitted(m1)
## X-squared = 8.0966, df = 8, p-value = 0.4241Now plot this Wheat zero/non-zero bionomal model to see outliers and the zeros vs non-zeros.
FIGURE 13: Apples zero/non-zero bionomal model to see outliers and zeros values vs non-zero values.
Checking for multi collinearity
## GVIF Df GVIF^(1/(2*Df))
## year NaN 14 NaN
## damagecause NaN 7 NaN
## county NaN 24 NaN
## damagecause:county NaN 168 NaN## pvalue
## year2003 3.591447e-02
## year2006 2.436066e-03
## year2008 7.423814e-06
## year2009 1.928975e-07
## year2010 6.395700e-05
## year2012 7.423814e-06
## year2013 1.358972e-11
## year2014 6.886671e-07
## year2015 4.184055e-06
## countyAsotin 9.075356e-03
## countyBenton 9.075356e-03
## countyColumbia 2.261309e-02
## countyGarfield 9.075356e-03
## countyGilliam 2.261309e-02
## countySherman 2.261309e-02
## countyUnion 2.261309e-02
## damagecauseHail:countyLincoln 4.935426e-02
## damagecauseHail:countyUnion 2.690240e-02Now subset to just those WHEAT observations with a loss greater than zero (so all non-zeros), and run a linear regression (switched to log loss due to outliers), to make sure that our residuals and other parameters suggest normality.
## Linear mixed model fit by REML ['lmerMod']
## Formula: log(loss) ~ year + damagecause + (1 | county)
## Data: subset(alllevs2_wheat, non_zero == 1)
##
## REML criterion at convergence: 7179.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6996 -0.5892 0.0703 0.6781 2.6628
##
## Random effects:
## Groups Name Variance Std.Dev.
## county (Intercept) 0.3674 0.6061
## Residual 2.4149 1.5540
## Number of obs: 1907, groups: county, 25
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 7.99724 0.22116 36.16
## year2002 0.43290 0.21176 2.04
## year2003 0.41796 0.22225 1.88
## year2004 0.27795 0.21310 1.30
## year2005 0.07724 0.21910 0.35
## year2006 0.68710 0.20185 3.40
## year2007 1.05394 0.21526 4.90
## year2008 1.69925 0.19843 8.56
## year2009 2.80687 0.19683 14.26
## year2010 1.03500 0.19983 5.18
## year2011 1.13875 0.20808 5.47
## year2012 1.08797 0.19821 5.49
## year2013 1.87594 0.19346 9.70
## year2014 2.09590 0.19745 10.61
## year2015 2.44563 0.19867 12.31
## damagecauseCold Winter -0.20275 0.15514 -1.31
## damagecauseDecline in Price 0.25623 0.15697 1.63
## damagecauseDrought 1.95038 0.14151 13.78
## damagecauseFreeze -0.07762 0.15223 -0.51
## damagecauseFrost 0.50660 0.15314 3.31
## damagecauseHail 0.60254 0.17121 3.52
## damagecauseHeat 1.11373 0.14213 7.84
Finally, we examine the Wheat model coefficent estimates of our model output.
Finally, we exponentiate the coefficient estimates and confidence intervals for odds ratios.
## rn lower upper estimate stderror
## 1: year2002 1.0199348 2.329465 1.5417217 1.235853
## 2: year2003 0.9846293 2.342657 1.5188577 1.248884
## 3: year2004 0.8715275 2.000847 1.3204231 1.237505
## 4: year2005 0.7046120 1.655988 1.0802969 1.244960
## 5: year2006 1.3410884 2.946764 1.9879437 1.223669
## 6: year2007 1.8851679 4.364643 2.8689339 1.240181
## 7: year2008 3.7132215 8.051724 5.4698321 1.219491
## 8: year2009 11.2766504 24.299239 16.5580431 1.217541
## 9: year2010 1.9063633 4.156021 2.8151147 1.221200
## 10: year2011 2.0809961 4.684967 3.1228698 1.231308
## 11: year2012 2.0161733 4.367868 2.9682470 1.219224
## 12: year2013 4.4739001 9.514839 6.5269495 1.213436
## 13: year2014 5.5310440 11.948051 8.1327549 1.218291
## 14: year2015 7.8275618 16.990224 11.5377976 1.219778
## 15: damagecauseCold Winter 0.6034317 1.105113 0.8164788 1.167822
## 16: damagecauseDecline in Price 0.9516170 1.755407 1.2920471 1.169963
## 17: damagecauseDrought 5.3360108 9.266054 7.0313553 1.152010
## 18: damagecauseFreeze 0.6878481 1.245579 0.9253126 1.164423
## 19: damagecauseFrost 1.2314893 2.237926 1.6596402 1.165488
## 20: damagecauseHail 1.3083016 2.550886 1.8267442 1.186738
## 21: damagecauseHeat 2.3086575 4.018848 3.0457065 1.152731
## rn lower upper estimate stderror
Hurdle Model - BARLEY
Here we run our hurdle technique for BARLEY, using a generalized linear model with a binomal function to delineate between zero and non-zero values. Given this model, Is our data normally distributed? What (if any) outliers exist? Are residuals well distributed - indicating normality?
## llh llhNull G2 McFadden r2ML
## -830.2168952 -1274.2283306 888.0228708 0.3484552 0.3448349
## r2CU
## 0.4906170##
## Hosmer and Lemeshow goodness of fit (GOF) test
##
## data: alllevs2_barley$non_zero, fitted(m1)
## X-squared = 7.0557, df = 8, p-value = 0.5306Now plot this Barley zero/non-zero bionomal model to see outliers and the zeros vs non-zeros.
FIGURE 13: barley zero/non-zero bionomal model to see outliers and zeros values vs non-zero values.
Checking for multi collinearity
## GVIF Df GVIF^(1/(2*Df))
## year 1.095000e+00 14 1.003
## damagecause 5.566929e+14 6 16.936
## county 3.703215e+30 19 6.374
## damagecause:county 1.804773e+44 114 1.564## pvalue
## (Intercept) 0.0042218704
## year2003 0.0494564652
## year2008 0.0338124241
## year2011 0.0342321549
## year2012 0.0338124241
## year2013 0.0004580656
## year2014 0.0002584132
## year2015 0.0001431552
## damagecauseDrought 0.0012138649
## damagecauseHeat 0.0027620640
## countyWhitman 0.0121281074
## damagecauseDrought:countyBenewah 0.0197675663Now subset to just those barley observations with a loss greater than zero (so all non-zeros), and run a linear regression (switched to log loss due to outliers), to make sure that our residuals and other parameters suggest normality.
## Linear mixed model fit by REML ['lmerMod']
## Formula: log(loss) ~ year + damagecause + (1 | county)
## Data: subset(alllevs2_barley, non_zero == 1)
##
## REML criterion at convergence: 2293.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5822 -0.5317 0.1089 0.6977 2.9113
##
## Random effects:
## Groups Name Variance Std.Dev.
## county (Intercept) 0.3238 0.569
## Residual 2.2462 1.499
## Number of obs: 620, groups: county, 20
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 7.92934 0.38828 20.421
## year2002 -0.10634 0.34844 -0.305
## year2003 0.18599 0.33325 0.558
## year2004 -0.85257 0.39113 -2.180
## year2005 -0.04265 0.36706 -0.116
## year2006 -0.67856 0.35936 -1.888
## year2007 0.19545 0.34292 0.570
## year2008 0.68248 0.33231 2.054
## year2009 -0.26571 0.36026 -0.738
## year2010 -0.66140 0.39697 -1.666
## year2011 0.55102 0.42699 1.290
## year2012 0.01274 0.33960 0.038
## year2013 0.72816 0.32320 2.253
## year2014 1.04415 0.32439 3.219
## year2015 0.96512 0.32545 2.965
## damagecauseDecline in Price -0.64825 0.33577 -1.931
## damagecauseDrought 0.77748 0.28135 2.763
## damagecauseFreeze -1.08850 0.44696 -2.435
## damagecauseFrost -0.24419 0.31581 -0.773
## damagecauseHail -0.01171 0.33567 -0.035
## damagecauseHeat 0.10291 0.28018 0.367
Finally, we examine the barley coefficent estimates of our model output.
Finally, we exponentiate the coefficient estimates and confidence intervals for odds ratios.
## rn lower upper estimate stderror
## 1: year2002 0.4584066 1.7605818 0.8991226 1.416849
## 2: year2003 0.6321075 2.2901168 1.2044047 1.395502
## 3: year2004 0.2004571 0.9074481 0.4263185 1.478646
## 4: year2005 0.4717765 1.9461020 0.9582494 1.443487
## 5: year2006 0.2532232 1.0145485 0.5073495 1.432413
## 6: year2007 0.6270592 2.3565104 1.2158574 1.409051
## 7: year2008 1.0416272 3.7573689 1.9787809 1.394188
## 8: year2009 0.3822009 1.5360223 0.7666618 1.433706
## 9: year2010 0.2396960 1.1099469 0.5161300 1.487307
## 10: year2011 0.7609116 3.9557706 1.7350299 1.532637
## 11: year2012 0.5242805 1.9495624 1.0128235 1.404386
## 12: year2013 1.1092485 3.8636135 2.0712759 1.381541
## 13: year2014 1.5155203 5.3101823 2.8409961 1.383185
## 14: year2015 1.3982636 4.9167324 2.6250936 1.384655
## 15: damagecauseDecline in Price 0.2736152 1.0003041 0.5229615 1.399019
## 16: damagecauseDrought 1.2645497 3.7467576 2.1759737 1.324912
## 17: damagecauseFreeze 0.1420929 0.7978644 0.3367214 1.563556
## 18: damagecauseFrost 0.4260330 1.4421351 0.7833419 1.371369
## 19: damagecauseHail 0.5173943 1.8921438 0.9883601 1.398874
## 20: damagecauseHeat 0.6456397 1.9046675 1.1083912 1.323372
Hurdle Model - CHERRIES
Here we run our hurdle technique for CHERRIES, using a generalized linear model with a binomal function to delineate between zero and non-zero values. Given this model, Is our data normally distributed? What (if any) outliers exist? Are residuals well distributed - indicating normality?
## llh llhNull G2 McFadden r2ML
## -317.8075409 -487.9400087 340.2649356 0.3486750 0.3705731
## r2CU
## 0.5042351##
## Hosmer and Lemeshow goodness of fit (GOF) test
##
## data: alllevs2_cherries$non_zero, fitted(m1)
## X-squared = 20.237, df = 8, p-value = 0.009476Now plot this Cherries zero/non-zero bionomal model to see outliers and the zeros vs non-zeros.
FIGURE 13: Cherries zero/non-zero bionomal model to see outliers and zeros values vs non-zero values.
Checking for multi collinearity
## GVIF Df GVIF^(1/(2*Df))
## year 1.234000e+00 14 1.008
## damagecause 8.692688e+04 6 2.580
## county 3.305766e+04 6 2.380
## damagecause:county 5.530000e+08 36 1.323## pvalue
## year2002 3.815859e-02
## year2005 1.078964e-02
## year2007 2.057694e-02
## year2008 5.511963e-03
## year2009 1.960629e-06
## year2010 3.116683e-07
## year2011 1.354410e-04
## year2012 1.960629e-06
## year2013 1.204504e-07
## year2014 1.135127e-05
## year2015 2.202546e-09
## damagecauseCold Winter 1.681518e-04
## damagecauseDecline in Price 4.792657e-03
## damagecauseHail 1.380223e-02
## damagecauseHeat 4.739288e-04
## countyDouglas 3.612953e-02
## countyWalla Walla 1.532929e-03
## countyWasco 1.380223e-02
## damagecauseHeat:countyGrant 3.199587e-02
## damagecauseDecline in Price:countyWalla Walla 4.255465e-02
## damagecauseHail:countyWalla Walla 3.705870e-02
## damagecauseCold Winter:countyWasco 1.761933e-02Now subset to just those Cherries observations with a loss greater than zero (so all non-zeros), and run a linear regression (switched to log loss due to outliers), to make sure that our residuals and other parameters suggest normality.
## Linear mixed model fit by REML ['lmerMod']
## Formula: log(loss) ~ year + damagecause + (1 | county)
## Data: subset(alllevs2_cherries, non_zero == 1)
##
## REML criterion at convergence: 948
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.5506 -0.5865 0.1251 0.6044 2.5611
##
## Random effects:
## Groups Name Variance Std.Dev.
## county (Intercept) 0.1767 0.4203
## Residual 1.7597 1.3265
## Number of obs: 279, groups: county, 7
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 8.8975 0.6014 14.794
## year2002 0.4859 0.6666 0.729
## year2003 -0.2252 0.6993 -0.322
## year2004 0.3002 0.6823 0.440
## year2005 0.7762 0.6516 1.191
## year2006 0.2667 0.7449 0.358
## year2007 1.3422 0.6609 2.031
## year2008 1.8676 0.6515 2.867
## year2009 2.2442 0.6122 3.666
## year2010 1.8473 0.6089 3.034
## year2011 1.7326 0.6319 2.742
## year2012 1.3609 0.6121 2.223
## year2013 1.8619 0.6059 3.073
## year2014 1.4657 0.6231 2.353
## year2015 1.6261 0.6012 2.705
## damagecauseCold Winter -0.8428 0.4203 -2.005
## damagecauseDecline in Price -0.7787 0.3262 -2.387
## damagecauseFreeze 0.2005 0.2504 0.801
## damagecauseFrost 0.2548 0.2463 1.034
## damagecauseHail -0.1646 0.3335 -0.493
## damagecauseHeat -0.1494 0.3562 -0.419
Finally, we examine the CHERRIES coefficent estimates of our model output.
Finally, we exponentiate the coefficient estimates and confidence intervals for odds ratios.
## rn lower upper estimate stderror
## 1: year2002 0.4579564 5.7241649 1.6256831 1.947578
## 2: year2003 0.2114117 2.9908863 0.7983585 2.012342
## 3: year2004 0.3693361 4.8986198 1.3501489 1.978472
## 4: year2005 0.6318880 7.4534131 2.1732859 1.918605
## 5: year2006 0.3177707 5.3375694 1.3055893 2.106231
## 6: year2007 1.0841355 13.3103324 3.8275486 1.936572
## 7: year2008 1.8709743 22.1246612 6.4724737 1.918374
## 8: year2009 2.9385413 29.9419903 9.4329147 1.844500
## 9: year2010 1.9845527 19.9962618 6.3427459 1.838396
## 10: year2011 1.6896045 18.6131204 5.6554231 1.881220
## 11: year2012 1.2072879 12.3600508 3.8996338 1.844241
## 12: year2013 2.0259930 20.1784870 6.4361657 1.832928
## 13: year2014 1.3239984 14.0376305 4.3307515 1.864617
## 14: year2015 1.6110876 15.7936317 5.0842582 1.824390
## 15: damagecauseCold Winter 0.1942672 0.9539478 0.4305199 1.522409
## 16: damagecauseDecline in Price 0.2478992 0.8533862 0.4589818 1.385738
## 17: damagecauseFreeze 0.7610356 1.9642748 1.2219719 1.284503
## 18: damagecauseFrost 0.8103128 2.0604915 1.2901959 1.279313
## 19: damagecauseHail 0.4523570 1.6032650 0.8482521 1.395835
## 20: damagecauseHeat 0.4394820 1.6949052 0.8612501 1.427956
Hurdle Model - DRY PEAS
Here we run our hurdle technique for DRY PEAS, using a generalized linear model with a binomal function to delineate between zero and non-zero values. Given this model, Is our data normally distributed? What (if any) outliers exist? Are residuals well distributed - indicating normality?
## llh llhNull G2 McFadden r2ML
## -679.8268582 -1138.2908423 916.9279682 0.4027652 0.3620367
## r2CU
## 0.5384221##
## Hosmer and Lemeshow goodness of fit (GOF) test
##
## data: alllevs2_drypeas$non_zero, fitted(m1)
## X-squared = 9.2597, df = 8, p-value = 0.3209Now plot this Dry Peas zero/non-zero bionomal model to see outliers and the zeros vs non-zeros.
FIGURE 13: Dry Peas zero/non-zero bionomal model to see outliers and zeros values vs non-zero values.
Checking for multi collinearity
## GVIF Df GVIF^(1/(2*Df))
## year NaN 14 NaN
## damagecause NaN 7 NaN
## county NaN 16 NaN
## damagecause:county NaN 112 NaN##
## Call:
## glm(formula = non_zero ~ year + damagecause * county, family = binomial(link = logit),
## data = alllevs2_drypeas)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.35061 -0.56960 -0.20076 -0.00002 2.86220
##
## Coefficients:
## Estimate Std. Error
## (Intercept) -3.894e+00 1.104e+00
## year2002 4.163e-01 4.093e-01
## year2003 5.682e-01 4.052e-01
## year2004 -1.251e+00 4.957e-01
## year2005 9.201e-01 3.971e-01
## year2006 1.179e+00 3.924e-01
## year2007 6.416e-01 4.033e-01
## year2008 1.422e+00 3.890e-01
## year2009 7.133e-01 4.016e-01
## year2010 1.654e+00 3.865e-01
## year2011 -1.850e-01 4.304e-01
## year2012 7.133e-01 4.016e-01
## year2013 1.985e+00 3.845e-01
## year2014 2.412e+00 3.847e-01
## year2015 2.359e+00 3.845e-01
## damagecauseCold Winter -1.686e+01 2.614e+03
## damagecauseDecline in Price -1.686e+01 2.614e+03
## damagecauseDrought 2.158e+00 1.216e+00
## damagecauseFreeze -1.686e+01 2.614e+03
## damagecauseFrost -1.686e+01 2.614e+03
## damagecauseHail 8.209e-01 1.325e+00
## damagecauseHeat 1.787e+00 1.233e+00
## countyBenewah 2.497e+00 1.207e+00
## countyClearwater 5.266e-14 1.500e+00
## countyColumbia 4.326e-14 1.500e+00
## countyGarfield 2.547e-14 1.500e+00
## countyGrant 6.770e-14 1.500e+00
## countyIdaho 1.787e+00 1.233e+00
## countyKootenai 1.787e+00 1.233e+00
## countyLatah 2.497e+00 1.207e+00
## countyLewis 3.462e+00 1.208e+00
## countyLincoln -1.686e+01 2.614e+03
## countyNez Perce 2.158e+00 1.216e+00
## countySpokane 2.158e+00 1.216e+00
## countyUmatilla 3.461e-14 1.500e+00
## countyUnion -1.686e+01 2.614e+03
## countyWalla Walla 1.360e+00 1.263e+00
## countyWhitman 4.180e+00 1.238e+00
## damagecauseCold Winter:countyBenewah -2.497e+00 3.697e+03
## damagecauseDecline in Price:countyBenewah 1.518e+01 2.614e+03
## damagecauseDrought:countyBenewah -1.192e+00 1.462e+00
## damagecauseFreeze:countyBenewah 1.436e+01 2.614e+03
## damagecauseFrost:countyBenewah 1.615e+01 2.614e+03
## damagecauseHail:countyBenewah -1.531e+00 1.574e+00
## damagecauseHeat:countyBenewah -8.216e-01 1.476e+00
## damagecauseCold Winter:countyClearwater 6.998e-08 3.697e+03
## damagecauseDecline in Price:countyClearwater 1.822e+01 2.614e+03
## damagecauseDrought:countyClearwater 2.022e+00 1.733e+00
## damagecauseFreeze:countyClearwater -1.838e-07 3.697e+03
## damagecauseFrost:countyClearwater 1.686e+01 2.614e+03
## damagecauseHail:countyClearwater 5.389e-01 1.830e+00
## damagecauseHeat:countyClearwater 3.705e-01 1.731e+00
## damagecauseCold Winter:countyColumbia 1.686e+01 2.614e+03
## damagecauseDecline in Price:countyColumbia 1.822e+01 2.614e+03
## damagecauseDrought:countyColumbia 1.647e+00 1.720e+00
## damagecauseFreeze:countyColumbia 1.686e+01 2.614e+03
## damagecauseFrost:countyColumbia 1.686e+01 2.614e+03
## damagecauseHail:countyColumbia 5.389e-01 1.830e+00
## damagecauseHeat:countyColumbia 2.017e+00 1.732e+00
## damagecauseCold Winter:countyGarfield 7.002e-08 3.697e+03
## damagecauseDecline in Price:countyGarfield 1.768e+01 2.614e+03
## damagecauseDrought:countyGarfield -7.980e-01 1.753e+00
## damagecauseFreeze:countyGarfield -1.837e-07 3.697e+03
## damagecauseFrost:countyGarfield 3.264e-08 3.697e+03
## damagecauseHail:countyGarfield -1.768e+01 2.614e+03
## damagecauseHeat:countyGarfield 7.097e-01 1.724e+00
## damagecauseCold Winter:countyGrant 6.999e-08 3.697e+03
## damagecauseDecline in Price:countyGrant 1.453e-09 3.697e+03
## damagecauseDrought:countyGrant -1.902e+01 2.614e+03
## damagecauseFreeze:countyGrant -1.838e-07 3.697e+03
## damagecauseFrost:countyGrant 1.822e+01 2.614e+03
## damagecauseHail:countyGrant -8.209e-01 2.001e+00
## damagecauseHeat:countyGrant -6.521e-14 1.743e+00
## damagecauseCold Winter:countyIdaho 1.589e+01 2.614e+03
## damagecauseDecline in Price:countyIdaho 1.589e+01 2.614e+03
## damagecauseDrought:countyIdaho -1.407e-01 1.492e+00
## damagecauseFreeze:countyIdaho -1.787e+00 3.697e+03
## damagecauseFrost:countyIdaho 1.589e+01 2.614e+03
## damagecauseHail:countyIdaho 5.302e-01 1.571e+00
## damagecauseHeat:countyIdaho -1.120e-01 1.498e+00
## damagecauseCold Winter:countyKootenai -1.787e+00 3.697e+03
## damagecauseDecline in Price:countyKootenai -1.787e+00 3.697e+03
## damagecauseDrought:countyKootenai -2.585e+00 1.530e+00
## damagecauseFreeze:countyKootenai -1.787e+00 3.697e+03
## damagecauseFrost:countyKootenai 1.507e+01 2.614e+03
## damagecauseHail:countyKootenai -1.947e+01 2.614e+03
## damagecauseHeat:countyKootenai -1.417e+00 1.505e+00
## damagecauseCold Winter:countyLatah 1.518e+01 2.614e+03
## damagecauseDecline in Price:countyLatah 1.572e+01 2.614e+03
## damagecauseDrought:countyLatah 5.184e-01 1.569e+00
## damagecauseFreeze:countyLatah 1.615e+01 2.614e+03
## damagecauseFrost:countyLatah 1.652e+01 2.614e+03
## damagecauseHail:countyLatah -8.209e-01 1.554e+00
## damagecauseHeat:countyLatah 3.331e-01 1.527e+00
## damagecauseCold Winter:countyLewis 1.476e+01 2.614e+03
## damagecauseDecline in Price:countyLewis 1.476e+01 2.614e+03
## damagecauseDrought:countyLewis -1.003e+00 1.514e+00
## damagecauseFreeze:countyLewis 1.340e+01 2.614e+03
## damagecauseFrost:countyLewis 1.476e+01 2.614e+03
## damagecauseHail:countyLewis -1.787e+00 1.554e+00
## damagecauseHeat:countyLewis -7.671e-02 1.582e+00
## damagecauseCold Winter:countyLincoln 3.372e+01 3.697e+03
## damagecauseDecline in Price:countyLincoln 3.454e+01 3.697e+03
## damagecauseDrought:countyLincoln 1.649e+01 2.614e+03
## damagecauseFreeze:countyLincoln 3.372e+01 3.697e+03
## damagecauseFrost:countyLincoln 1.686e+01 4.528e+03
## damagecauseHail:countyLincoln -8.209e-01 3.697e+03
## damagecauseHeat:countyLincoln 1.643e+01 2.614e+03
## damagecauseCold Winter:countyNez Perce 1.552e+01 2.614e+03
## damagecauseDecline in Price:countyNez Perce 1.606e+01 2.614e+03
## damagecauseDrought:countyNez Perce 3.018e-01 1.521e+00
## damagecauseFreeze:countyNez Perce 1.606e+01 2.614e+03
## damagecauseFrost:countyNez Perce 1.649e+01 2.614e+03
## damagecauseHail:countyNez Perce -1.587e-01 1.558e+00
## damagecauseHeat:countyNez Perce 6.723e-01 1.535e+00
## damagecauseCold Winter:countySpokane -2.158e+00 3.697e+03
## damagecauseDecline in Price:countySpokane 1.606e+01 2.614e+03
## damagecauseDrought:countySpokane 8.575e-01 1.576e+00
## damagecauseFreeze:countySpokane 1.552e+01 2.614e+03
## damagecauseFrost:countySpokane 1.606e+01 2.614e+03
## damagecauseHail:countySpokane -8.209e-01 1.568e+00
## damagecauseHeat:countySpokane 2.351e-01 1.507e+00
## damagecauseCold Winter:countyUmatilla 6.999e-08 3.697e+03
## damagecauseDecline in Price:countyUmatilla 1.440e-09 3.697e+03
## damagecauseDrought:countyUmatilla 6.622e-01 1.709e+00
## damagecauseFreeze:countyUmatilla 1.768e+01 2.614e+03
## damagecauseFrost:countyUmatilla 1.822e+01 2.614e+03
## damagecauseHail:countyUmatilla -8.209e-01 2.001e+00
## damagecauseHeat:countyUmatilla 1.675e+00 1.725e+00
## damagecauseCold Winter:countyUnion 3.372e+01 3.697e+03
## damagecauseDecline in Price:countyUnion 1.686e+01 4.528e+03
## damagecauseDrought:countyUnion -2.158e+00 3.697e+03
## damagecauseFreeze:countyUnion 1.686e+01 4.528e+03
## damagecauseFrost:countyUnion 3.508e+01 3.697e+03
## damagecauseHail:countyUnion 1.740e+01 2.614e+03
## damagecauseHeat:countyUnion 1.686e+01 2.614e+03
## damagecauseCold Winter:countyWalla Walla -1.360e+00 3.697e+03
## damagecauseDecline in Price:countyWalla Walla 1.686e+01 2.614e+03
## damagecauseDrought:countyWalla Walla -5.503e-02 1.509e+00
## damagecauseFreeze:countyWalla Walla 1.632e+01 2.614e+03
## damagecauseFrost:countyWalla Walla 1.632e+01 2.614e+03
## damagecauseHail:countyWalla Walla -2.295e-02 1.605e+00
## damagecauseHeat:countyWalla Walla 1.470e+00 1.573e+00
## damagecauseCold Winter:countyWhitman 1.447e+01 2.614e+03
## damagecauseDecline in Price:countyWhitman 1.404e+01 2.614e+03
## damagecauseDrought:countyWhitman -1.165e+00 1.591e+00
## damagecauseFreeze:countyWhitman 1.268e+01 2.614e+03
## damagecauseFrost:countyWhitman 1.484e+01 2.614e+03
## damagecauseHail:countyWhitman -1.538e+00 1.577e+00
## damagecauseHeat:countyWhitman -1.350e+00 1.550e+00
## z value Pr(>|z|)
## (Intercept) -3.527 0.000420 ***
## year2002 1.017 0.309124
## year2003 1.402 0.160813
## year2004 -2.523 0.011643 *
## year2005 2.317 0.020501 *
## year2006 3.004 0.002664 **
## year2007 1.591 0.111684
## year2008 3.656 0.000256 ***
## year2009 1.776 0.075696 .
## year2010 4.278 1.88e-05 ***
## year2011 -0.430 0.667327
## year2012 1.776 0.075696 .
## year2013 5.163 2.44e-07 ***
## year2014 6.269 3.63e-10 ***
## year2015 6.135 8.53e-10 ***
## damagecauseCold Winter -0.006 0.994854
## damagecauseDecline in Price -0.006 0.994854
## damagecauseDrought 1.775 0.075951 .
## damagecauseFreeze -0.006 0.994854
## damagecauseFrost -0.006 0.994854
## damagecauseHail 0.620 0.535559
## damagecauseHeat 1.450 0.147070
## countyBenewah 2.069 0.038535 *
## countyClearwater 0.000 1.000000
## countyColumbia 0.000 1.000000
## countyGarfield 0.000 1.000000
## countyGrant 0.000 1.000000
## countyIdaho 1.450 0.147070
## countyKootenai 1.450 0.147070
## countyLatah 2.069 0.038535 *
## countyLewis 2.865 0.004165 **
## countyLincoln -0.006 0.994854
## countyNez Perce 1.775 0.075951 .
## countySpokane 1.775 0.075951 .
## countyUmatilla 0.000 1.000000
## countyUnion -0.006 0.994854
## countyWalla Walla 1.077 0.281667
## countyWhitman 3.377 0.000732 ***
## damagecauseCold Winter:countyBenewah -0.001 0.999461
## damagecauseDecline in Price:countyBenewah 0.006 0.995366
## damagecauseDrought:countyBenewah -0.815 0.414808
## damagecauseFreeze:countyBenewah 0.005 0.995616
## damagecauseFrost:countyBenewah 0.006 0.995071
## damagecauseHail:countyBenewah -0.972 0.330959
## damagecauseHeat:countyBenewah -0.557 0.577764
## damagecauseCold Winter:countyClearwater 0.000 1.000000
## damagecauseDecline in Price:countyClearwater 0.007 0.994439
## damagecauseDrought:countyClearwater 1.167 0.243350
## damagecauseFreeze:countyClearwater 0.000 1.000000
## damagecauseFrost:countyClearwater 0.006 0.994854
## damagecauseHail:countyClearwater 0.294 0.768463
## damagecauseHeat:countyClearwater 0.214 0.830481
## damagecauseCold Winter:countyColumbia 0.006 0.994854
## damagecauseDecline in Price:countyColumbia 0.007 0.994439
## damagecauseDrought:countyColumbia 0.957 0.338470
## damagecauseFreeze:countyColumbia 0.006 0.994854
## damagecauseFrost:countyColumbia 0.006 0.994854
## damagecauseHail:countyColumbia 0.294 0.768463
## damagecauseHeat:countyColumbia 1.164 0.244299
## damagecauseCold Winter:countyGarfield 0.000 1.000000
## damagecauseDecline in Price:countyGarfield 0.007 0.994604
## damagecauseDrought:countyGarfield -0.455 0.648911
## damagecauseFreeze:countyGarfield 0.000 1.000000
## damagecauseFrost:countyGarfield 0.000 1.000000
## damagecauseHail:countyGarfield -0.007 0.994604
## damagecauseHeat:countyGarfield 0.412 0.680639
## damagecauseCold Winter:countyGrant 0.000 1.000000
## damagecauseDecline in Price:countyGrant 0.000 1.000000
## damagecauseDrought:countyGrant -0.007 0.994196
## damagecauseFreeze:countyGrant 0.000 1.000000
## damagecauseFrost:countyGrant 0.007 0.994439
## damagecauseHail:countyGrant -0.410 0.681693
## damagecauseHeat:countyGrant 0.000 1.000000
## damagecauseCold Winter:countyIdaho 0.006 0.995149
## damagecauseDecline in Price:countyIdaho 0.006 0.995149
## damagecauseDrought:countyIdaho -0.094 0.924867
## damagecauseFreeze:countyIdaho 0.000 0.999614
## damagecauseFrost:countyIdaho 0.006 0.995149
## damagecauseHail:countyIdaho 0.337 0.735788
## damagecauseHeat:countyIdaho -0.075 0.940408
## damagecauseCold Winter:countyKootenai 0.000 0.999614
## damagecauseDecline in Price:countyKootenai 0.000 0.999614
## damagecauseDrought:countyKootenai -1.689 0.091178 .
## damagecauseFreeze:countyKootenai 0.000 0.999614
## damagecauseFrost:countyKootenai 0.006 0.995400
## damagecauseHail:countyKootenai -0.007 0.994058
## damagecauseHeat:countyKootenai -0.942 0.346419
## damagecauseCold Winter:countyLatah 0.006 0.995366
## damagecauseDecline in Price:countyLatah 0.006 0.995201
## damagecauseDrought:countyLatah 0.330 0.741127
## damagecauseFreeze:countyLatah 0.006 0.995071
## damagecauseFrost:countyLatah 0.006 0.994958
## damagecauseHail:countyLatah -0.528 0.597231
## damagecauseHeat:countyLatah 0.218 0.827319
## damagecauseCold Winter:countyLewis 0.006 0.995496
## damagecauseDecline in Price:countyLewis 0.006 0.995496
## damagecauseDrought:countyLewis -0.663 0.507626
## damagecauseFreeze:countyLewis 0.005 0.995911
## damagecauseFrost:countyLewis 0.006 0.995496
## damagecauseHail:countyLewis -1.149 0.250436
## damagecauseHeat:countyLewis -0.048 0.961340
## damagecauseCold Winter:countyLincoln 0.009 0.992723
## damagecauseDecline in Price:countyLincoln 0.009 0.992546
## damagecauseDrought:countyLincoln 0.006 0.994967
## damagecauseFreeze:countyLincoln 0.009 0.992723
## damagecauseFrost:countyLincoln 0.004 0.997029
## damagecauseHail:countyLincoln 0.000 0.999823
## damagecauseHeat:countyLincoln 0.006 0.994985
## damagecauseCold Winter:countyNez Perce 0.006 0.995262
## damagecauseDecline in Price:countyNez Perce 0.006 0.995098
## damagecauseDrought:countyNez Perce 0.198 0.842734
## damagecauseFreeze:countyNez Perce 0.006 0.995098
## damagecauseFrost:countyNez Perce 0.006 0.994967
## damagecauseHail:countyNez Perce -0.102 0.918856
## damagecauseHeat:countyNez Perce 0.438 0.661340
## damagecauseCold Winter:countySpokane -0.001 0.999534
## damagecauseDecline in Price:countySpokane 0.006 0.995098
## damagecauseDrought:countySpokane 0.544 0.586466
## damagecauseFreeze:countySpokane 0.006 0.995262
## damagecauseFrost:countySpokane 0.006 0.995098
## damagecauseHail:countySpokane -0.523 0.600637
## damagecauseHeat:countySpokane 0.156 0.876061
## damagecauseCold Winter:countyUmatilla 0.000 1.000000
## damagecauseDecline in Price:countyUmatilla 0.000 1.000000
## damagecauseDrought:countyUmatilla 0.387 0.698416
## damagecauseFreeze:countyUmatilla 0.007 0.994604
## damagecauseFrost:countyUmatilla 0.007 0.994439
## damagecauseHail:countyUmatilla -0.410 0.681693
## damagecauseHeat:countyUmatilla 0.971 0.331477
## damagecauseCold Winter:countyUnion 0.009 0.992723
## damagecauseDecline in Price:countyUnion 0.004 0.997029
## damagecauseDrought:countyUnion -0.001 0.999534
## damagecauseFreeze:countyUnion 0.004 0.997029
## damagecauseFrost:countyUnion 0.009 0.992429
## damagecauseHail:countyUnion 0.007 0.994690
## damagecauseHeat:countyUnion 0.006 0.994854
## damagecauseCold Winter:countyWalla Walla 0.000 0.999707
## damagecauseDecline in Price:countyWalla Walla 0.006 0.994854
## damagecauseDrought:countyWalla Walla -0.036 0.970915
## damagecauseFreeze:countyWalla Walla 0.006 0.995019
## damagecauseFrost:countyWalla Walla 0.006 0.995019
## damagecauseHail:countyWalla Walla -0.014 0.988596
## damagecauseHeat:countyWalla Walla 0.935 0.349923
## damagecauseCold Winter:countyWhitman 0.006 0.995584
## damagecauseDecline in Price:countyWhitman 0.005 0.995715
## damagecauseDrought:countyWhitman -0.732 0.464127
## damagecauseFreeze:countyWhitman 0.005 0.996130
## damagecauseFrost:countyWhitman 0.006 0.995471
## damagecauseHail:countyWhitman -0.975 0.329327
## damagecauseHeat:countyWhitman -0.871 0.383744
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2276.6 on 2039 degrees of freedom
## Residual deviance: 1359.7 on 1890 degrees of freedom
## AIC: 1659.7
##
## Number of Fisher Scoring iterations: 18Now subset to just those Dry Peas observations with a loss greater than zero (so all non-zeros), and run a linear regression (switched to log loss due to outliers), to make sure that our residuals and other parameters suggest normality.
## Linear mixed model fit by REML ['lmerMod']
## Formula: log(loss) ~ year + damagecause + (1 | county)
## Data: subset(alllevs2_drypeas, non_zero == 1)
##
## REML criterion at convergence: 1860
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9544 -0.4928 0.1551 0.6655 2.1097
##
## Random effects:
## Groups Name Variance Std.Dev.
## county (Intercept) 0.3996 0.6321
## Residual 2.2811 1.5103
## Number of obs: 502, groups: county, 17
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 6.4011 0.4337 14.758
## year2002 1.1477 0.4605 2.492
## year2003 1.7577 0.4493 3.912
## year2004 1.6750 0.6272 2.670
## year2005 2.2060 0.4360 5.059
## year2006 1.3581 0.4271 3.180
## year2007 1.6262 0.4486 3.625
## year2008 2.4535 0.4210 5.828
## year2009 1.8246 0.4456 4.095
## year2010 2.3902 0.4191 5.703
## year2011 2.0400 0.5166 3.949
## year2012 2.2563 0.4510 5.003
## year2013 2.4718 0.4136 5.977
## year2014 2.9396 0.4059 7.243
## year2015 3.8526 0.4023 9.577
## damagecauseCold Winter -0.6207 0.4355 -1.425
## damagecauseDecline in Price -0.4614 0.3677 -1.255
## damagecauseDrought 0.4783 0.2587 1.849
## damagecauseFreeze -0.9689 0.4255 -2.277
## damagecauseFrost -0.2361 0.3297 -0.716
## damagecauseHail 0.3804 0.2905 1.309
## damagecauseHeat 0.2298 0.2515 0.914
Finally, we examine the DRY PEAS coefficent estimates of our model output.
Finally, we exponentiate the coefficient estimates and confidence intervals for odds ratios.
## rn lower upper estimate stderror
## 1: year2002 1.3017723 7.6412632 3.1510220 1.584912
## 2: year2003 2.4469410 13.7523548 5.7990471 1.567200
## 3: year2004 1.6018655 17.8527384 5.3388800 1.872447
## 4: year2005 3.9293215 20.9850703 9.0796703 1.546574
## 5: year2006 1.7129457 8.8396657 3.8887481 1.532749
## 6: year2007 2.1497273 12.0563155 5.0844397 1.566053
## 7: year2008 5.1830773 26.1285021 11.6295078 1.523426
## 8: year2009 2.6352492 14.5996543 6.2000068 1.561365
## 9: year2010 4.8811790 24.4259125 10.9157261 1.520577
## 10: year2011 2.8537106 20.8210658 7.6903393 1.676387
## 11: year2012 4.0176232 22.7341095 9.5473067 1.569822
## 12: year2013 5.3546238 26.2384348 11.8432900 1.512191
## 13: year2014 8.6741820 41.2573245 18.9087670 1.500614
## 14: year2015 21.7649829 102.1191780 47.1175633 1.495241
## 15: damagecauseCold Winter 0.2330977 1.2458334 0.5375878 1.545689
## 16: damagecauseDecline in Price 0.3109437 1.2771526 0.6304087 1.444388
## 17: damagecauseDrought 0.9812936 2.6511404 1.6132606 1.295214
## 18: damagecauseFreeze 0.1677002 0.8607936 0.3795095 1.530426
## 19: damagecauseFrost 0.4194035 1.4890046 0.7897253 1.390562
## 20: damagecauseHail 0.8377201 2.5599627 1.4629353 1.337147
## 21: damagecauseHeat 0.7758169 2.0391972 1.2582955 1.285938
## rn lower upper estimate stderror